Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long t, i = 0, j = 0;
  while (~scanf("%ld", &t)) {
    for (i = 1; (i) * (i + 1) / 2 + (j) * (j + 1) / 2 <= t; i++) {
      for (j = i; (i) * (i + 1) / 2 + (j) * (j + 1) / 2 <= t; j++) {
        if ((i) * (i + 1) / 2 + (j) * (j + 1) / 2 == t) {
          printf("YES\n");
          return 0;
        }
      }
      j = 0;
    }
    printf("NO\n");
  }
  return 0;
}